%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU271+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:47 EDT 2023 % Result : Theorem 13.17s 2.49s % Output : Proof 26.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEU271+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Wed Aug 23 17:02:11 EDT 2023 % 0.10/0.30 % CPUTime : % 0.15/0.52 ________ _____ % 0.15/0.52 ___ __ \_________(_)________________________________ % 0.15/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.52 % 0.15/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.52 (2023-06-19) % 0.15/0.52 % 0.15/0.52 (c) Philipp Rümmer, 2009-2023 % 0.15/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.52 Amanda Stjerna. % 0.15/0.52 Free software under BSD-3-Clause. % 0.15/0.52 % 0.15/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.52 % 0.15/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.15/0.53 Running up to 7 provers in parallel. % 0.15/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.31/0.99 Prover 1: Preprocessing ... % 2.31/1.00 Prover 4: Preprocessing ... % 2.80/1.02 Prover 5: Preprocessing ... % 2.80/1.02 Prover 6: Preprocessing ... % 2.80/1.02 Prover 0: Preprocessing ... % 2.80/1.02 Prover 2: Preprocessing ... % 2.80/1.02 Prover 3: Preprocessing ... % 6.10/1.52 Prover 1: Warning: ignoring some quantifiers % 6.10/1.58 Prover 5: Proving ... % 6.86/1.59 Prover 1: Constructing countermodel ... % 6.86/1.60 Prover 3: Warning: ignoring some quantifiers % 6.86/1.61 Prover 2: Proving ... % 6.86/1.61 Prover 4: Warning: ignoring some quantifiers % 6.86/1.61 Prover 6: Proving ... % 7.09/1.62 Prover 3: Constructing countermodel ... % 7.09/1.66 Prover 4: Constructing countermodel ... % 7.66/1.76 Prover 0: Proving ... % 9.25/1.94 Prover 3: gave up % 9.25/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.87/2.00 Prover 7: Preprocessing ... % 9.87/2.11 Prover 7: Warning: ignoring some quantifiers % 9.87/2.11 Prover 1: gave up % 9.87/2.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.87/2.12 Prover 7: Constructing countermodel ... % 9.87/2.20 Prover 8: Preprocessing ... % 12.33/2.39 Prover 8: Warning: ignoring some quantifiers % 12.82/2.43 Prover 8: Constructing countermodel ... % 13.17/2.49 Prover 0: proved (1951ms) % 13.17/2.49 % 13.17/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.17/2.49 % 13.17/2.50 Prover 6: stopped % 13.17/2.50 Prover 2: stopped % 13.17/2.50 Prover 5: stopped % 13.17/2.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.17/2.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.17/2.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.17/2.53 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.72/2.56 Prover 10: Preprocessing ... % 13.72/2.57 Prover 13: Preprocessing ... % 13.72/2.57 Prover 11: Preprocessing ... % 14.00/2.58 Prover 16: Preprocessing ... % 14.00/2.61 Prover 10: Warning: ignoring some quantifiers % 14.00/2.62 Prover 10: Constructing countermodel ... % 14.44/2.64 Prover 16: Warning: ignoring some quantifiers % 14.44/2.64 Prover 16: Constructing countermodel ... % 14.60/2.68 Prover 13: Warning: ignoring some quantifiers % 14.60/2.69 Prover 13: Constructing countermodel ... % 15.11/2.72 Prover 10: gave up % 15.11/2.74 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.45/2.78 Prover 19: Preprocessing ... % 15.45/2.82 Prover 11: Warning: ignoring some quantifiers % 15.45/2.82 Prover 8: gave up % 15.45/2.83 Prover 11: Constructing countermodel ... % 15.45/2.91 Prover 19: Warning: ignoring some quantifiers % 15.45/2.92 Prover 19: Constructing countermodel ... % 19.67/3.36 Prover 19: gave up % 22.51/3.81 Prover 13: gave up % 25.77/4.26 Prover 11: Found proof (size 103) % 25.77/4.26 Prover 11: proved (1766ms) % 25.77/4.26 Prover 16: stopped % 25.77/4.26 Prover 4: stopped % 25.77/4.27 Prover 7: stopped % 25.77/4.27 % 25.77/4.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.77/4.27 % 26.35/4.27 % SZS output start Proof for theBenchmark % 26.35/4.28 Assumptions after simplification: % 26.35/4.28 --------------------------------- % 26.35/4.28 % 26.35/4.28 (d10_xboole_0) % 26.35/4.30 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ $i(v1) | % 26.35/4.30 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0: $i] % 26.35/4.30 : ! [v1: $i] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 26.35/4.30 ? [v2: int] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0: $i] : ! [v1: % 26.35/4.30 int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 26.35/4.30 % 26.35/4.30 (d12_relat_2) % 26.35/4.31 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_field(v0) = v1) | ~ $i(v0) | ? % 26.35/4.31 [v2: int] : ? [v3: int] : ? [v4: int] : (( ~ (v2 = 0) & relation(v0) = v2) % 26.35/4.31 | (((v4 = 0 & is_antisymmetric_in(v0, v1) = 0) | ( ~ (v3 = 0) & % 26.35/4.31 antisymmetric(v0) = v3)) & ((v3 = 0 & antisymmetric(v0) = 0) | ( ~ % 26.35/4.31 (v4 = 0) & is_antisymmetric_in(v0, v1) = v4))))) & ! [v0: $i] : ! % 26.35/4.31 [v1: any] : ( ~ (antisymmetric(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: % 26.35/4.31 $i] : ? [v4: int] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | % 26.35/4.31 (v4 = 0 & relation_field(v0) = v3 & is_antisymmetric_in(v0, v3) = 0 & % 26.35/4.31 $i(v3))) & (v1 = 0 | ( ~ (v4 = 0) & relation_field(v0) = v3 & % 26.35/4.31 is_antisymmetric_in(v0, v3) = v4 & $i(v3)))))) & ! [v0: $i] : ( ~ % 26.35/4.31 (relation(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? [v3: int] : % 26.35/4.31 (((v3 = 0 & relation_field(v0) = v2 & is_antisymmetric_in(v0, v2) = 0 & % 26.35/4.31 $i(v2)) | ( ~ (v1 = 0) & antisymmetric(v0) = v1)) & ((v1 = 0 & % 26.35/4.31 antisymmetric(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & % 26.35/4.31 is_antisymmetric_in(v0, v2) = v3 & $i(v2))))) % 26.35/4.31 % 26.35/4.31 (d1_wellord2) % 26.35/4.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.35/4.32 $i] : ( ~ (inclusion_relation(v0) = v1) | ~ (ordered_pair(v3, v4) = v5) | % 26.35/4.32 ~ (relation_field(v1) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) % 26.35/4.32 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : (( ~ (v7 = 0) % 26.35/4.32 & in(v4, v0) = v7) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & % 26.35/4.32 in(v3, v0) = v6) | (((v9 = 0 & subset(v3, v4) = 0) | ( ~ (v8 = 0) & % 26.35/4.32 in(v5, v1) = v8)) & ((v8 = 0 & in(v5, v1) = 0) | ( ~ (v9 = 0) & % 26.35/4.32 subset(v3, v4) = v9))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.35/4.32 ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (inclusion_relation(v0) = v1) | % 26.35/4.32 ~ (relation_field(v1) = v2) | ~ (subset(v3, v4) = v5) | ~ $i(v4) | ~ % 26.35/4.32 $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: $i] : % 26.35/4.32 ? [v9: int] : (( ~ (v7 = 0) & in(v4, v0) = v7) | ( ~ (v6 = 0) & % 26.35/4.32 relation(v1) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (( ~ (v5 = 0) | % 26.35/4.32 (v9 = 0 & ordered_pair(v3, v4) = v8 & in(v8, v1) = 0 & $i(v8))) & (v5 % 26.35/4.32 = 0 | ( ~ (v9 = 0) & ordered_pair(v3, v4) = v8 & in(v8, v1) = v9 & % 26.35/4.32 $i(v8)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | % 26.35/4.32 ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ~ $i(v1) | % 26.35/4.32 ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? % 26.35/4.32 [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ($i(v5) & $i(v4) & % 26.35/4.32 ((v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & % 26.35/4.32 subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, % 26.35/4.32 v1) = 0 & $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( % 26.35/4.32 ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 26.35/4.32 $i(v8)))) | ( ~ (v3 = 0) & relation(v1) = v3)))) & ! [v0: $i] : % 26.35/4.32 ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ % 26.35/4.32 (relation_field(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = % 26.35/4.32 0) & relation(v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 26.35/4.32 (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ % 26.35/4.32 $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: % 26.35/4.33 int] : ? [v8: $i] : ? [v9: int] : ? [v10: int] : ($i(v5) & $i(v4) & ( ~ % 26.35/4.33 (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 & ! [v11: $i] : ! [v12: % 26.35/4.33 $i] : ! [v13: $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ $i(v12) % 26.35/4.33 | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: int] : ? % 26.35/4.33 [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ (v14 = 0) & % 26.35/4.33 in(v11, v0) = v14) | (((v17 = 0 & subset(v11, v12) = 0) | ( ~ % 26.35/4.33 (v16 = 0) & in(v13, v1) = v16)) & ((v16 = 0 & in(v13, v1) = % 26.35/4.33 0) | ( ~ (v17 = 0) & subset(v11, v12) = v17))))) & ! [v11: % 26.35/4.33 $i] : ! [v12: $i] : ! [v13: any] : ( ~ (subset(v11, v12) = v13) | % 26.35/4.33 ~ $i(v12) | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? [v16: % 26.35/4.33 $i] : ? [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = v15) | ( ~ % 26.35/4.33 (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v17 = 0 & % 26.35/4.33 ordered_pair(v11, v12) = v16 & in(v16, v1) = 0 & $i(v16))) & % 26.35/4.33 (v13 = 0 | ( ~ (v17 = 0) & ordered_pair(v11, v12) = v16 & % 26.35/4.33 in(v16, v1) = v17 & $i(v16)))))))) & (v2 = v1 | (v7 = 0 & v6 % 26.35/4.33 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = % 26.35/4.33 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0 & % 26.35/4.33 $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 = 0) & % 26.35/4.33 ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & $i(v8)))) | ( ~ (v3 % 26.35/4.33 = v0) & relation_field(v1) = v3 & $i(v3))))) % 26.35/4.33 % 26.35/4.33 (d4_relat_2) % 26.35/4.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 26.35/4.33 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_antisymmetric_in(v0, v1) = 0) | ~ % 26.35/4.33 (relation(v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 26.35/4.33 int] : ? [v6: int] : ? [v7: $i] : ? [v8: int] : ? [v9: int] : (( ~ (v9 % 26.35/4.33 = 0) & in(v4, v0) = v9) | ( ~ (v8 = 0) & ordered_pair(v2, v3) = v7 & % 26.35/4.33 in(v7, v0) = v8 & $i(v7)) | ( ~ (v6 = 0) & in(v3, v1) = v6) | ( ~ (v5 = % 26.35/4.33 0) & in(v2, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.35/4.33 [v3: $i] : ! [v4: $i] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ % 26.35/4.33 (is_antisymmetric_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ $i(v3) | ~ % 26.35/4.33 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] % 26.35/4.33 : ? [v8: $i] : ? [v9: int] : (( ~ (v9 = 0) & ordered_pair(v3, v2) = v8 & % 26.35/4.33 in(v8, v0) = v9 & $i(v8)) | ( ~ (v7 = 0) & in(v4, v0) = v7) | ( ~ (v6 = % 26.35/4.33 0) & in(v3, v1) = v6) | ( ~ (v5 = 0) & in(v2, v1) = v5))) & ! [v0: % 26.35/4.33 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (is_antisymmetric_in(v0, v1) % 26.35/4.33 = v2) | ~ (relation(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 26.35/4.33 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v4 = v3) & ordered_pair(v4, v3) % 26.35/4.33 = v6 & ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & % 26.35/4.33 in(v4, v1) = 0 & in(v3, v1) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3))) % 26.35/4.33 % 26.35/4.33 (d6_relat_1) % 26.35/4.33 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 26.35/4.33 int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & % 26.35/4.33 relation_rng(v0) = v4 & relation_field(v0) = v3 & set_union2(v1, v4) = % 26.35/4.33 v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0: % 26.35/4.33 $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: int] : % 26.35/4.33 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & relation_dom(v0) = v4 % 26.35/4.33 & relation_field(v0) = v3 & set_union2(v4, v1) = v3 & $i(v4) & $i(v3)) | % 26.35/4.33 ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.35/4.33 (relation_field(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: % 26.35/4.33 $i] : ? [v5: $i] : ((v5 = v1 & relation_dom(v0) = v3 & relation_rng(v0) = % 26.35/4.33 v4 & set_union2(v3, v4) = v1 & $i(v4) & $i(v3) & $i(v1)) | ( ~ (v2 = 0) % 26.35/4.33 & relation(v0) = v2))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 26.35/4.33 $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & % 26.35/4.33 relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 % 26.35/4.33 & $i(v3) & $i(v2) & $i(v1))) % 26.35/4.33 % 26.35/4.33 (dt_k1_wellord2) % 26.35/4.33 ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_relation(v0) = v1) | ~ $i(v0) | % 26.35/4.33 relation(v1) = 0) % 26.35/4.33 % 26.35/4.33 (t5_wellord2) % 26.35/4.34 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 26.35/4.34 inclusion_relation(v0) = v1 & antisymmetric(v1) = v2 & $i(v1) & $i(v0)) % 26.35/4.34 % 26.35/4.34 (function-axioms) % 26.35/4.34 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.35/4.34 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & % 26.35/4.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.35/4.34 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 26.35/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.35/4.34 : (v1 = v0 | ~ (is_antisymmetric_in(v3, v2) = v1) | ~ % 26.35/4.34 (is_antisymmetric_in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.35/4.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 26.35/4.34 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 26.35/4.34 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ % 26.35/4.34 (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.35/4.34 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 26.35/4.34 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.35/4.34 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = % 26.35/4.34 v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.35/4.34 (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 26.35/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.35/4.34 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = % 26.35/4.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 26.35/4.34 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : ! % 26.35/4.34 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ % 26.35/4.34 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 26.35/4.34 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 26.35/4.34 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ % 26.35/4.34 (inclusion_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.35/4.34 (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! % 26.35/4.34 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 26.35/4.34 | ~ (antisymmetric(v2) = v1) | ~ (antisymmetric(v2) = v0)) & ! [v0: % 26.35/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.35/4.34 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: % 26.35/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.35/4.34 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 26.35/4.34 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 26.35/4.34 (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: % 26.35/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.35/4.34 ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : % 26.35/4.34 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 26.35/4.34 (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: % 26.35/4.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 26.35/4.34 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] % 26.35/4.34 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 26.35/4.34 ~ (empty(v2) = v0)) % 26.35/4.34 % 26.35/4.34 Further assumptions not needed in the proof: % 26.35/4.34 -------------------------------------------- % 26.35/4.34 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc2_funct_1, cc2_ordinal1, % 26.35/4.34 cc3_ordinal1, commutativity_k2_tarski, commutativity_k2_xboole_0, d5_tarski, % 26.35/4.34 dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, % 26.35/4.34 dt_k2_tarski, dt_k2_xboole_0, dt_k3_relat_1, dt_k4_tarski, dt_m1_subset_1, % 26.35/4.34 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_ordinal1, fc2_xboole_0, % 26.35/4.34 fc3_xboole_0, idempotence_k2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_xboole_0, % 26.35/4.34 rc2_funct_1, rc2_ordinal1, rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc4_funct_1, % 26.35/4.34 reflexivity_r1_tarski, t1_boole, t1_subset, t2_subset, t3_subset, t4_subset, % 26.35/4.34 t5_subset, t6_boole, t7_boole, t8_boole % 26.35/4.34 % 26.35/4.34 Those formulas are unsatisfiable: % 26.35/4.34 --------------------------------- % 26.35/4.34 % 26.35/4.34 Begin of proof % 26.35/4.34 | % 26.35/4.34 | ALPHA: (d10_xboole_0) implies: % 26.35/4.35 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ~ % 26.35/4.35 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subset(v0, v1) = % 26.35/4.35 | v2)) % 26.35/4.35 | % 26.35/4.35 | ALPHA: (d12_relat_2) implies: % 26.35/4.35 | (2) ! [v0: $i] : ! [v1: any] : ( ~ (antisymmetric(v0) = v1) | ~ $i(v0) | % 26.35/4.35 | ? [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v2 = 0) & % 26.35/4.35 | relation(v0) = v2) | (( ~ (v1 = 0) | (v4 = 0 & relation_field(v0) % 26.35/4.35 | = v3 & is_antisymmetric_in(v0, v3) = 0 & $i(v3))) & (v1 = 0 | % 26.35/4.35 | ( ~ (v4 = 0) & relation_field(v0) = v3 & % 26.35/4.35 | is_antisymmetric_in(v0, v3) = v4 & $i(v3)))))) % 26.35/4.35 | % 26.35/4.35 | ALPHA: (d1_wellord2) implies: % 26.35/4.35 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (inclusion_relation(v0) = % 26.35/4.35 | v2) | ~ (relation(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 26.35/4.35 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: $i] % 26.35/4.35 | : ? [v9: int] : ? [v10: int] : ($i(v5) & $i(v4) & ( ~ (v2 = v1) | % 26.35/4.35 | (v3 = v0 & relation_field(v1) = v0 & ! [v11: $i] : ! [v12: $i] % 26.35/4.35 | : ! [v13: $i] : ( ~ (ordered_pair(v11, v12) = v13) | ~ % 26.35/4.35 | $i(v12) | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? % 26.35/4.35 | [v16: int] : ? [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = % 26.35/4.35 | v15) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (((v17 = 0 & % 26.35/4.35 | subset(v11, v12) = 0) | ( ~ (v16 = 0) & in(v13, v1) = % 26.35/4.35 | v16)) & ((v16 = 0 & in(v13, v1) = 0) | ( ~ (v17 = 0) % 26.35/4.35 | & subset(v11, v12) = v17))))) & ! [v11: $i] : ! % 26.35/4.35 | [v12: $i] : ! [v13: any] : ( ~ (subset(v11, v12) = v13) | ~ % 26.35/4.35 | $i(v12) | ~ $i(v11) | ? [v14: int] : ? [v15: int] : ? % 26.35/4.35 | [v16: $i] : ? [v17: int] : (( ~ (v15 = 0) & in(v12, v0) = % 26.35/4.35 | v15) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = % 26.35/4.35 | 0) | (v17 = 0 & ordered_pair(v11, v12) = v16 & % 26.35/4.35 | in(v16, v1) = 0 & $i(v16))) & (v13 = 0 | ( ~ (v17 = % 26.35/4.35 | 0) & ordered_pair(v11, v12) = v16 & in(v16, v1) = % 26.35/4.35 | v17 & $i(v16)))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & % 26.35/4.35 | in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = % 26.35/4.35 | 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0 & % 26.35/4.35 | $i(v8))) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 % 26.35/4.35 | = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9 & % 26.35/4.35 | $i(v8)))) | ( ~ (v3 = v0) & relation_field(v1) = v3 & % 26.35/4.35 | $i(v3))))) % 26.35/4.35 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ % 26.35/4.35 | (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ % 26.35/4.35 | $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & relation(v1) = % 26.35/4.35 | v3)) % 26.35/4.35 | % 26.35/4.36 | ALPHA: (d4_relat_2) implies: % 26.35/4.36 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 26.35/4.36 | (is_antisymmetric_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ % 26.35/4.36 | $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 26.35/4.36 | [v6: $i] : ( ~ (v4 = v3) & ordered_pair(v4, v3) = v6 & % 26.35/4.36 | ordered_pair(v3, v4) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & % 26.35/4.36 | in(v4, v1) = 0 & in(v3, v1) = 0 & $i(v6) & $i(v5) & $i(v4) & % 26.35/4.36 | $i(v3))) % 26.35/4.36 | % 26.35/4.36 | ALPHA: (d6_relat_1) implies: % 26.35/4.36 | (6) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 26.35/4.36 | [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v2 & relation_rng(v0) = % 26.35/4.36 | v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1 & $i(v3) & % 26.35/4.36 | $i(v2) & $i(v1))) % 26.35/4.36 | % 26.35/4.36 | ALPHA: (function-axioms) implies: % 26.35/4.36 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.35/4.36 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 26.35/4.36 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 26.35/4.36 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 26.35/4.36 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.35/4.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 26.35/4.36 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.35/4.36 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 26.35/4.36 | v2) = v0)) % 26.35/4.36 | % 26.35/4.36 | DELTA: instantiating (t5_wellord2) with fresh symbols all_48_0, all_48_1, % 26.35/4.36 | all_48_2 gives: % 26.35/4.36 | (11) ~ (all_48_0 = 0) & inclusion_relation(all_48_2) = all_48_1 & % 26.35/4.36 | antisymmetric(all_48_1) = all_48_0 & $i(all_48_1) & $i(all_48_2) % 26.35/4.36 | % 26.35/4.36 | ALPHA: (11) implies: % 26.35/4.36 | (12) ~ (all_48_0 = 0) % 26.35/4.36 | (13) $i(all_48_2) % 26.35/4.36 | (14) $i(all_48_1) % 26.35/4.36 | (15) antisymmetric(all_48_1) = all_48_0 % 26.35/4.36 | (16) inclusion_relation(all_48_2) = all_48_1 % 26.35/4.36 | % 26.35/4.36 | GROUND_INST: instantiating (2) with all_48_1, all_48_0, simplifying with (14), % 26.35/4.36 | (15) gives: % 26.35/4.36 | (17) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (( ~ (v0 = 0) & % 26.35/4.36 | relation(all_48_1) = v0) | (( ~ (all_48_0 = 0) | (v2 = 0 & % 26.35/4.36 | relation_field(all_48_1) = v1 & is_antisymmetric_in(all_48_1, % 26.35/4.36 | v1) = 0 & $i(v1))) & (all_48_0 = 0 | ( ~ (v2 = 0) & % 26.35/4.36 | relation_field(all_48_1) = v1 & is_antisymmetric_in(all_48_1, % 26.35/4.36 | v1) = v2 & $i(v1))))) % 26.35/4.36 | % 26.35/4.37 | GROUND_INST: instantiating (dt_k1_wellord2) with all_48_2, all_48_1, % 26.35/4.37 | simplifying with (13), (16) gives: % 26.35/4.37 | (18) relation(all_48_1) = 0 % 26.35/4.37 | % 26.35/4.37 | DELTA: instantiating (17) with fresh symbols all_95_0, all_95_1, all_95_2 % 26.35/4.37 | gives: % 26.35/4.37 | (19) ( ~ (all_95_2 = 0) & relation(all_48_1) = all_95_2) | (( ~ (all_48_0 = % 26.35/4.37 | 0) | (all_95_0 = 0 & relation_field(all_48_1) = all_95_1 & % 26.35/4.37 | is_antisymmetric_in(all_48_1, all_95_1) = 0 & $i(all_95_1))) & % 26.35/4.37 | (all_48_0 = 0 | ( ~ (all_95_0 = 0) & relation_field(all_48_1) = % 26.35/4.37 | all_95_1 & is_antisymmetric_in(all_48_1, all_95_1) = all_95_0 & % 26.35/4.37 | $i(all_95_1)))) % 26.35/4.37 | % 26.35/4.37 | BETA: splitting (19) gives: % 26.35/4.37 | % 26.35/4.37 | Case 1: % 26.35/4.37 | | % 26.35/4.37 | | (20) ~ (all_95_2 = 0) & relation(all_48_1) = all_95_2 % 26.35/4.37 | | % 26.35/4.37 | | ALPHA: (20) implies: % 26.35/4.37 | | (21) ~ (all_95_2 = 0) % 26.35/4.37 | | (22) relation(all_48_1) = all_95_2 % 26.35/4.37 | | % 26.35/4.37 | | GROUND_INST: instantiating (7) with 0, all_95_2, all_48_1, simplifying with % 26.35/4.37 | | (18), (22) gives: % 26.35/4.37 | | (23) all_95_2 = 0 % 26.35/4.37 | | % 26.35/4.37 | | REDUCE: (21), (23) imply: % 26.35/4.37 | | (24) $false % 26.35/4.37 | | % 26.35/4.37 | | CLOSE: (24) is inconsistent. % 26.35/4.37 | | % 26.35/4.37 | Case 2: % 26.35/4.37 | | % 26.35/4.37 | | (25) ( ~ (all_48_0 = 0) | (all_95_0 = 0 & relation_field(all_48_1) = % 26.35/4.37 | | all_95_1 & is_antisymmetric_in(all_48_1, all_95_1) = 0 & % 26.35/4.37 | | $i(all_95_1))) & (all_48_0 = 0 | ( ~ (all_95_0 = 0) & % 26.35/4.37 | | relation_field(all_48_1) = all_95_1 & % 26.35/4.37 | | is_antisymmetric_in(all_48_1, all_95_1) = all_95_0 & % 26.35/4.37 | | $i(all_95_1))) % 26.35/4.37 | | % 26.35/4.37 | | ALPHA: (25) implies: % 26.35/4.37 | | (26) all_48_0 = 0 | ( ~ (all_95_0 = 0) & relation_field(all_48_1) = % 26.35/4.37 | | all_95_1 & is_antisymmetric_in(all_48_1, all_95_1) = all_95_0 & % 26.35/4.37 | | $i(all_95_1)) % 26.35/4.37 | | % 26.35/4.37 | | BETA: splitting (26) gives: % 26.35/4.37 | | % 26.35/4.37 | | Case 1: % 26.35/4.37 | | | % 26.35/4.37 | | | (27) all_48_0 = 0 % 26.35/4.37 | | | % 26.35/4.37 | | | REDUCE: (12), (27) imply: % 26.35/4.37 | | | (28) $false % 26.35/4.37 | | | % 26.35/4.37 | | | CLOSE: (28) is inconsistent. % 26.35/4.37 | | | % 26.35/4.37 | | Case 2: % 26.35/4.37 | | | % 26.35/4.37 | | | (29) ~ (all_95_0 = 0) & relation_field(all_48_1) = all_95_1 & % 26.35/4.37 | | | is_antisymmetric_in(all_48_1, all_95_1) = all_95_0 & $i(all_95_1) % 26.35/4.37 | | | % 26.35/4.37 | | | ALPHA: (29) implies: % 26.35/4.37 | | | (30) ~ (all_95_0 = 0) % 26.35/4.37 | | | (31) $i(all_95_1) % 26.35/4.37 | | | (32) is_antisymmetric_in(all_48_1, all_95_1) = all_95_0 % 26.35/4.37 | | | (33) relation_field(all_48_1) = all_95_1 % 26.35/4.37 | | | % 26.35/4.37 | | | GROUND_INST: instantiating (3) with all_48_2, all_48_1, all_48_1, % 26.35/4.37 | | | simplifying with (13), (14), (16), (18) gives: % 26.35/4.37 | | | (34) ? [v0: $i] : ? [v1: $i] : (relation_field(all_48_1) = all_48_2 & % 26.35/4.37 | | | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 26.35/4.37 | | | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: % 26.35/4.37 | | | int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : (( ~ (v6 % 26.35/4.37 | | | = 0) & in(v3, all_48_2) = v6) | ( ~ (v5 = 0) & in(v2, % 26.35/4.37 | | | all_48_2) = v5) | (((v8 = 0 & subset(v2, v3) = 0) | ( ~ % 26.35/4.38 | | | (v7 = 0) & in(v4, all_48_1) = v7)) & ((v7 = 0 & in(v4, % 26.35/4.38 | | | all_48_1) = 0) | ( ~ (v8 = 0) & subset(v2, v3) = % 26.35/4.38 | | | v8))))) & ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( % 26.35/4.38 | | | ~ (subset(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] % 26.35/4.38 | | | : ? [v6: int] : ? [v7: $i] : ? [v8: int] : (( ~ (v6 = 0) & % 26.35/4.38 | | | in(v3, all_48_2) = v6) | ( ~ (v5 = 0) & in(v2, all_48_2) = % 26.35/4.38 | | | v5) | (( ~ (v4 = 0) | (v8 = 0 & ordered_pair(v2, v3) = v7 % 26.35/4.38 | | | & in(v7, all_48_1) = 0 & $i(v7))) & (v4 = 0 | ( ~ (v8 % 26.35/4.38 | | | = 0) & ordered_pair(v2, v3) = v7 & in(v7, all_48_1) % 26.35/4.38 | | | = v8 & $i(v7))))))) % 26.35/4.38 | | | % 26.35/4.38 | | | GROUND_INST: instantiating (6) with all_48_1, simplifying with (14), (18) % 26.35/4.38 | | | gives: % 26.35/4.38 | | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_48_1) % 26.35/4.38 | | | = v1 & relation_rng(all_48_1) = v2 & relation_field(all_48_1) = % 26.35/4.38 | | | v0 & set_union2(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0)) % 26.35/4.38 | | | % 26.35/4.38 | | | GROUND_INST: instantiating (5) with all_48_1, all_95_1, all_95_0, % 26.35/4.38 | | | simplifying with (14), (18), (31), (32) gives: % 26.35/4.38 | | | (36) all_95_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 26.35/4.38 | | | $i] : ( ~ (v1 = v0) & ordered_pair(v1, v0) = v3 & % 26.35/4.38 | | | ordered_pair(v0, v1) = v2 & in(v3, all_48_1) = 0 & in(v2, % 26.35/4.38 | | | all_48_1) = 0 & in(v1, all_95_1) = 0 & in(v0, all_95_1) = 0 & % 26.35/4.38 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.35/4.38 | | | % 26.35/4.38 | | | GROUND_INST: instantiating (4) with all_48_2, all_48_1, all_95_1, % 26.35/4.38 | | | simplifying with (13), (14), (16), (33) gives: % 26.35/4.38 | | | (37) all_95_1 = all_48_2 | ? [v0: int] : ( ~ (v0 = 0) & % 26.35/4.38 | | | relation(all_48_1) = v0) % 26.35/4.38 | | | % 26.35/4.38 | | | DELTA: instantiating (35) with fresh symbols all_148_0, all_148_1, % 26.35/4.38 | | | all_148_2 gives: % 26.35/4.38 | | | (38) relation_dom(all_48_1) = all_148_1 & relation_rng(all_48_1) = % 26.35/4.38 | | | all_148_0 & relation_field(all_48_1) = all_148_2 & % 26.35/4.38 | | | set_union2(all_148_1, all_148_0) = all_148_2 & $i(all_148_0) & % 26.35/4.38 | | | $i(all_148_1) & $i(all_148_2) % 26.35/4.38 | | | % 26.35/4.38 | | | ALPHA: (38) implies: % 26.35/4.38 | | | (39) relation_field(all_48_1) = all_148_2 % 26.35/4.38 | | | % 26.35/4.38 | | | DELTA: instantiating (34) with fresh symbols all_156_0, all_156_1 gives: % 26.35/4.38 | | | (40) relation_field(all_48_1) = all_48_2 & $i(all_156_0) & % 26.35/4.38 | | | $i(all_156_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 26.35/4.38 | | | (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 26.35/4.38 | | | int] : ? [v4: int] : ? [v5: int] : ? [v6: int] : (( ~ (v4 = % 26.35/4.38 | | | 0) & in(v1, all_48_2) = v4) | ( ~ (v3 = 0) & in(v0, % 26.35/4.38 | | | all_48_2) = v3) | (((v6 = 0 & subset(v0, v1) = 0) | ( ~ % 26.35/4.38 | | | (v5 = 0) & in(v2, all_48_1) = v5)) & ((v5 = 0 & in(v2, % 26.35/4.38 | | | all_48_1) = 0) | ( ~ (v6 = 0) & subset(v0, v1) = % 26.35/4.38 | | | v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 26.35/4.38 | | | (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 26.35/4.38 | | | ? [v4: int] : ? [v5: $i] : ? [v6: int] : (( ~ (v4 = 0) & % 26.35/4.38 | | | in(v1, all_48_2) = v4) | ( ~ (v3 = 0) & in(v0, all_48_2) = % 26.35/4.38 | | | v3) | (( ~ (v2 = 0) | (v6 = 0 & ordered_pair(v0, v1) = v5 & % 26.35/4.38 | | | in(v5, all_48_1) = 0 & $i(v5))) & (v2 = 0 | ( ~ (v6 = 0) % 26.35/4.38 | | | & ordered_pair(v0, v1) = v5 & in(v5, all_48_1) = v6 & % 26.35/4.38 | | | $i(v5)))))) % 26.35/4.38 | | | % 26.35/4.38 | | | ALPHA: (40) implies: % 26.35/4.38 | | | (41) relation_field(all_48_1) = all_48_2 % 26.35/4.38 | | | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, % 26.35/4.38 | | | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 26.35/4.38 | | | int] : ? [v5: int] : ? [v6: int] : (( ~ (v4 = 0) & in(v1, % 26.35/4.38 | | | all_48_2) = v4) | ( ~ (v3 = 0) & in(v0, all_48_2) = v3) | % 26.35/4.38 | | | (((v6 = 0 & subset(v0, v1) = 0) | ( ~ (v5 = 0) & in(v2, % 26.35/4.38 | | | all_48_1) = v5)) & ((v5 = 0 & in(v2, all_48_1) = 0) | % 26.35/4.38 | | | ( ~ (v6 = 0) & subset(v0, v1) = v6))))) % 26.35/4.38 | | | % 26.35/4.38 | | | BETA: splitting (36) gives: % 26.35/4.38 | | | % 26.35/4.38 | | | Case 1: % 26.35/4.38 | | | | % 26.35/4.38 | | | | (43) all_95_0 = 0 % 26.35/4.38 | | | | % 26.35/4.38 | | | | REDUCE: (30), (43) imply: % 26.35/4.38 | | | | (44) $false % 26.35/4.38 | | | | % 26.35/4.38 | | | | CLOSE: (44) is inconsistent. % 26.35/4.38 | | | | % 26.35/4.38 | | | Case 2: % 26.35/4.38 | | | | % 26.35/4.38 | | | | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 % 26.35/4.38 | | | | = v0) & ordered_pair(v1, v0) = v3 & ordered_pair(v0, v1) = % 26.35/4.38 | | | | v2 & in(v3, all_48_1) = 0 & in(v2, all_48_1) = 0 & in(v1, % 26.35/4.38 | | | | all_95_1) = 0 & in(v0, all_95_1) = 0 & $i(v3) & $i(v2) & % 26.35/4.38 | | | | $i(v1) & $i(v0)) % 26.35/4.38 | | | | % 26.35/4.38 | | | | DELTA: instantiating (45) with fresh symbols all_166_0, all_166_1, % 26.35/4.38 | | | | all_166_2, all_166_3 gives: % 26.35/4.39 | | | | (46) ~ (all_166_2 = all_166_3) & ordered_pair(all_166_2, all_166_3) % 26.35/4.39 | | | | = all_166_0 & ordered_pair(all_166_3, all_166_2) = all_166_1 & % 26.35/4.39 | | | | in(all_166_0, all_48_1) = 0 & in(all_166_1, all_48_1) = 0 & % 26.35/4.39 | | | | in(all_166_2, all_95_1) = 0 & in(all_166_3, all_95_1) = 0 & % 26.35/4.39 | | | | $i(all_166_0) & $i(all_166_1) & $i(all_166_2) & $i(all_166_3) % 26.35/4.39 | | | | % 26.35/4.39 | | | | ALPHA: (46) implies: % 26.35/4.39 | | | | (47) ~ (all_166_2 = all_166_3) % 26.35/4.39 | | | | (48) $i(all_166_3) % 26.35/4.39 | | | | (49) $i(all_166_2) % 26.35/4.39 | | | | (50) in(all_166_3, all_95_1) = 0 % 26.35/4.39 | | | | (51) in(all_166_2, all_95_1) = 0 % 26.35/4.39 | | | | (52) in(all_166_1, all_48_1) = 0 % 26.35/4.39 | | | | (53) in(all_166_0, all_48_1) = 0 % 26.35/4.39 | | | | (54) ordered_pair(all_166_3, all_166_2) = all_166_1 % 26.35/4.39 | | | | (55) ordered_pair(all_166_2, all_166_3) = all_166_0 % 26.35/4.39 | | | | % 26.35/4.39 | | | | BETA: splitting (37) gives: % 26.35/4.39 | | | | % 26.35/4.39 | | | | Case 1: % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | (56) all_95_1 = all_48_2 % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | REDUCE: (51), (56) imply: % 26.35/4.39 | | | | | (57) in(all_166_2, all_48_2) = 0 % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | REDUCE: (50), (56) imply: % 26.35/4.39 | | | | | (58) in(all_166_3, all_48_2) = 0 % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | GROUND_INST: instantiating (42) with all_166_3, all_166_2, all_166_1, % 26.35/4.39 | | | | | simplifying with (48), (49), (54) gives: % 26.35/4.39 | | | | | (59) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : (( % 26.35/4.39 | | | | | ~ (v1 = 0) & in(all_166_2, all_48_2) = v1) | ( ~ (v0 = 0) % 26.35/4.39 | | | | | & in(all_166_3, all_48_2) = v0) | (((v3 = 0 & % 26.35/4.39 | | | | | subset(all_166_3, all_166_2) = 0) | ( ~ (v2 = 0) & % 26.35/4.39 | | | | | in(all_166_1, all_48_1) = v2)) & ((v2 = 0 & % 26.35/4.39 | | | | | in(all_166_1, all_48_1) = 0) | ( ~ (v3 = 0) & % 26.35/4.39 | | | | | subset(all_166_3, all_166_2) = v3)))) % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | GROUND_INST: instantiating (42) with all_166_2, all_166_3, all_166_0, % 26.35/4.39 | | | | | simplifying with (48), (49), (55) gives: % 26.35/4.39 | | | | | (60) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : (( % 26.35/4.39 | | | | | ~ (v1 = 0) & in(all_166_3, all_48_2) = v1) | ( ~ (v0 = 0) % 26.35/4.39 | | | | | & in(all_166_2, all_48_2) = v0) | (((v3 = 0 & % 26.35/4.39 | | | | | subset(all_166_2, all_166_3) = 0) | ( ~ (v2 = 0) & % 26.35/4.39 | | | | | in(all_166_0, all_48_1) = v2)) & ((v2 = 0 & % 26.35/4.39 | | | | | in(all_166_0, all_48_1) = 0) | ( ~ (v3 = 0) & % 26.35/4.39 | | | | | subset(all_166_2, all_166_3) = v3)))) % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | DELTA: instantiating (60) with fresh symbols all_222_0, all_222_1, % 26.35/4.39 | | | | | all_222_2, all_222_3 gives: % 26.35/4.39 | | | | | (61) ( ~ (all_222_2 = 0) & in(all_166_3, all_48_2) = all_222_2) | ( % 26.35/4.39 | | | | | ~ (all_222_3 = 0) & in(all_166_2, all_48_2) = all_222_3) | % 26.35/4.39 | | | | | (((all_222_0 = 0 & subset(all_166_2, all_166_3) = 0) | ( ~ % 26.35/4.39 | | | | | (all_222_1 = 0) & in(all_166_0, all_48_1) = all_222_1)) % 26.35/4.39 | | | | | & ((all_222_1 = 0 & in(all_166_0, all_48_1) = 0) | ( ~ % 26.35/4.39 | | | | | (all_222_0 = 0) & subset(all_166_2, all_166_3) = % 26.35/4.39 | | | | | all_222_0))) % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | DELTA: instantiating (59) with fresh symbols all_223_0, all_223_1, % 26.35/4.39 | | | | | all_223_2, all_223_3 gives: % 26.35/4.39 | | | | | (62) ( ~ (all_223_2 = 0) & in(all_166_2, all_48_2) = all_223_2) | ( % 26.35/4.39 | | | | | ~ (all_223_3 = 0) & in(all_166_3, all_48_2) = all_223_3) | % 26.35/4.39 | | | | | (((all_223_0 = 0 & subset(all_166_3, all_166_2) = 0) | ( ~ % 26.35/4.39 | | | | | (all_223_1 = 0) & in(all_166_1, all_48_1) = all_223_1)) % 26.35/4.39 | | | | | & ((all_223_1 = 0 & in(all_166_1, all_48_1) = 0) | ( ~ % 26.35/4.39 | | | | | (all_223_0 = 0) & subset(all_166_3, all_166_2) = % 26.35/4.39 | | | | | all_223_0))) % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | BETA: splitting (61) gives: % 26.35/4.39 | | | | | % 26.35/4.39 | | | | | Case 1: % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | (63) ~ (all_222_2 = 0) & in(all_166_3, all_48_2) = all_222_2 % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | ALPHA: (63) implies: % 26.35/4.39 | | | | | | (64) ~ (all_222_2 = 0) % 26.35/4.39 | | | | | | (65) in(all_166_3, all_48_2) = all_222_2 % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | GROUND_INST: instantiating (9) with 0, all_222_2, all_48_2, % 26.35/4.39 | | | | | | all_166_3, simplifying with (58), (65) gives: % 26.35/4.39 | | | | | | (66) all_222_2 = 0 % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | REDUCE: (64), (66) imply: % 26.35/4.39 | | | | | | (67) $false % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | CLOSE: (67) is inconsistent. % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | Case 2: % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | (68) ( ~ (all_222_3 = 0) & in(all_166_2, all_48_2) = all_222_3) | % 26.35/4.39 | | | | | | (((all_222_0 = 0 & subset(all_166_2, all_166_3) = 0) | ( ~ % 26.35/4.39 | | | | | | (all_222_1 = 0) & in(all_166_0, all_48_1) = % 26.35/4.39 | | | | | | all_222_1)) & ((all_222_1 = 0 & in(all_166_0, % 26.35/4.39 | | | | | | all_48_1) = 0) | ( ~ (all_222_0 = 0) & % 26.35/4.39 | | | | | | subset(all_166_2, all_166_3) = all_222_0))) % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | BETA: splitting (68) gives: % 26.35/4.39 | | | | | | % 26.35/4.39 | | | | | | Case 1: % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | (69) ~ (all_222_3 = 0) & in(all_166_2, all_48_2) = all_222_3 % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | ALPHA: (69) implies: % 26.35/4.39 | | | | | | | (70) ~ (all_222_3 = 0) % 26.35/4.39 | | | | | | | (71) in(all_166_2, all_48_2) = all_222_3 % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | GROUND_INST: instantiating (9) with 0, all_222_3, all_48_2, % 26.35/4.39 | | | | | | | all_166_2, simplifying with (57), (71) gives: % 26.35/4.39 | | | | | | | (72) all_222_3 = 0 % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | REDUCE: (70), (72) imply: % 26.35/4.39 | | | | | | | (73) $false % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | CLOSE: (73) is inconsistent. % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | Case 2: % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | (74) ((all_222_0 = 0 & subset(all_166_2, all_166_3) = 0) | ( ~ % 26.35/4.39 | | | | | | | (all_222_1 = 0) & in(all_166_0, all_48_1) = % 26.35/4.39 | | | | | | | all_222_1)) & ((all_222_1 = 0 & in(all_166_0, % 26.35/4.39 | | | | | | | all_48_1) = 0) | ( ~ (all_222_0 = 0) & % 26.35/4.39 | | | | | | | subset(all_166_2, all_166_3) = all_222_0)) % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | ALPHA: (74) implies: % 26.35/4.39 | | | | | | | (75) (all_222_0 = 0 & subset(all_166_2, all_166_3) = 0) | ( ~ % 26.35/4.39 | | | | | | | (all_222_1 = 0) & in(all_166_0, all_48_1) = all_222_1) % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | BETA: splitting (75) gives: % 26.35/4.39 | | | | | | | % 26.35/4.39 | | | | | | | Case 1: % 26.35/4.39 | | | | | | | | % 26.35/4.40 | | | | | | | | (76) all_222_0 = 0 & subset(all_166_2, all_166_3) = 0 % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | ALPHA: (76) implies: % 26.35/4.40 | | | | | | | | (77) subset(all_166_2, all_166_3) = 0 % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | BETA: splitting (62) gives: % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | Case 1: % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | (78) ~ (all_223_2 = 0) & in(all_166_2, all_48_2) = % 26.35/4.40 | | | | | | | | | all_223_2 % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | ALPHA: (78) implies: % 26.35/4.40 | | | | | | | | | (79) ~ (all_223_2 = 0) % 26.35/4.40 | | | | | | | | | (80) in(all_166_2, all_48_2) = all_223_2 % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_223_2, all_48_2, % 26.35/4.40 | | | | | | | | | all_166_2, simplifying with (57), (80) gives: % 26.35/4.40 | | | | | | | | | (81) all_223_2 = 0 % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | REDUCE: (79), (81) imply: % 26.35/4.40 | | | | | | | | | (82) $false % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | CLOSE: (82) is inconsistent. % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | Case 2: % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | (83) ( ~ (all_223_3 = 0) & in(all_166_3, all_48_2) = % 26.35/4.40 | | | | | | | | | all_223_3) | (((all_223_0 = 0 & subset(all_166_3, % 26.35/4.40 | | | | | | | | | all_166_2) = 0) | ( ~ (all_223_1 = 0) & % 26.35/4.40 | | | | | | | | | in(all_166_1, all_48_1) = all_223_1)) & % 26.35/4.40 | | | | | | | | | ((all_223_1 = 0 & in(all_166_1, all_48_1) = 0) | ( ~ % 26.35/4.40 | | | | | | | | | (all_223_0 = 0) & subset(all_166_3, all_166_2) = % 26.35/4.40 | | | | | | | | | all_223_0))) % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | BETA: splitting (83) gives: % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | | Case 1: % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | (84) ~ (all_223_3 = 0) & in(all_166_3, all_48_2) = % 26.35/4.40 | | | | | | | | | | all_223_3 % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | ALPHA: (84) implies: % 26.35/4.40 | | | | | | | | | | (85) ~ (all_223_3 = 0) % 26.35/4.40 | | | | | | | | | | (86) in(all_166_3, all_48_2) = all_223_3 % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_223_3, all_48_2, % 26.35/4.40 | | | | | | | | | | all_166_3, simplifying with (58), (86) gives: % 26.35/4.40 | | | | | | | | | | (87) all_223_3 = 0 % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | REDUCE: (85), (87) imply: % 26.35/4.40 | | | | | | | | | | (88) $false % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | CLOSE: (88) is inconsistent. % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | Case 2: % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | (89) ((all_223_0 = 0 & subset(all_166_3, all_166_2) = 0) % 26.35/4.40 | | | | | | | | | | | ( ~ (all_223_1 = 0) & in(all_166_1, all_48_1) = % 26.35/4.40 | | | | | | | | | | all_223_1)) & ((all_223_1 = 0 & in(all_166_1, % 26.35/4.40 | | | | | | | | | | all_48_1) = 0) | ( ~ (all_223_0 = 0) & % 26.35/4.40 | | | | | | | | | | subset(all_166_3, all_166_2) = all_223_0)) % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | ALPHA: (89) implies: % 26.35/4.40 | | | | | | | | | | (90) (all_223_0 = 0 & subset(all_166_3, all_166_2) = 0) | % 26.35/4.40 | | | | | | | | | | ( ~ (all_223_1 = 0) & in(all_166_1, all_48_1) = % 26.35/4.40 | | | | | | | | | | all_223_1) % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | BETA: splitting (90) gives: % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | Case 1: % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | (91) all_223_0 = 0 & subset(all_166_3, all_166_2) = 0 % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | ALPHA: (91) implies: % 26.35/4.40 | | | | | | | | | | | (92) subset(all_166_3, all_166_2) = 0 % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_166_2, all_166_3, % 26.35/4.40 | | | | | | | | | | | simplifying with (48), (49), (92) gives: % 26.35/4.40 | | | | | | | | | | | (93) all_166_2 = all_166_3 | ? [v0: int] : ( ~ (v0 = % 26.35/4.40 | | | | | | | | | | | 0) & subset(all_166_2, all_166_3) = v0) % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | BETA: splitting (93) gives: % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | Case 1: % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | (94) all_166_2 = all_166_3 % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | REDUCE: (47), (94) imply: % 26.35/4.40 | | | | | | | | | | | | (95) $false % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | CLOSE: (95) is inconsistent. % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | Case 2: % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | (96) ? [v0: int] : ( ~ (v0 = 0) & subset(all_166_2, % 26.35/4.40 | | | | | | | | | | | | all_166_3) = v0) % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | DELTA: instantiating (96) with fresh symbol all_365_0 % 26.35/4.40 | | | | | | | | | | | | gives: % 26.35/4.40 | | | | | | | | | | | | (97) ~ (all_365_0 = 0) & subset(all_166_2, all_166_3) % 26.35/4.40 | | | | | | | | | | | | = all_365_0 % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | ALPHA: (97) implies: % 26.35/4.40 | | | | | | | | | | | | (98) ~ (all_365_0 = 0) % 26.35/4.40 | | | | | | | | | | | | (99) subset(all_166_2, all_166_3) = all_365_0 % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_365_0, all_166_3, % 26.35/4.40 | | | | | | | | | | | | all_166_2, simplifying with (77), (99) gives: % 26.35/4.40 | | | | | | | | | | | | (100) all_365_0 = 0 % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | REDUCE: (98), (100) imply: % 26.35/4.40 | | | | | | | | | | | | (101) $false % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | | CLOSE: (101) is inconsistent. % 26.35/4.40 | | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | End of split % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | Case 2: % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | (102) ~ (all_223_1 = 0) & in(all_166_1, all_48_1) = % 26.35/4.40 | | | | | | | | | | | all_223_1 % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | ALPHA: (102) implies: % 26.35/4.40 | | | | | | | | | | | (103) ~ (all_223_1 = 0) % 26.35/4.40 | | | | | | | | | | | (104) in(all_166_1, all_48_1) = all_223_1 % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_223_1, all_48_1, % 26.35/4.40 | | | | | | | | | | | all_166_1, simplifying with (52), (104) gives: % 26.35/4.40 | | | | | | | | | | | (105) all_223_1 = 0 % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | REDUCE: (103), (105) imply: % 26.35/4.40 | | | | | | | | | | | (106) $false % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | | CLOSE: (106) is inconsistent. % 26.35/4.40 | | | | | | | | | | | % 26.35/4.40 | | | | | | | | | | End of split % 26.35/4.40 | | | | | | | | | | % 26.35/4.40 | | | | | | | | | End of split % 26.35/4.40 | | | | | | | | | % 26.35/4.40 | | | | | | | | End of split % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | Case 2: % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | (107) ~ (all_222_1 = 0) & in(all_166_0, all_48_1) = % 26.35/4.40 | | | | | | | | all_222_1 % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | ALPHA: (107) implies: % 26.35/4.40 | | | | | | | | (108) ~ (all_222_1 = 0) % 26.35/4.40 | | | | | | | | (109) in(all_166_0, all_48_1) = all_222_1 % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_222_1, all_48_1, % 26.35/4.40 | | | | | | | | all_166_0, simplifying with (53), (109) gives: % 26.35/4.40 | | | | | | | | (110) all_222_1 = 0 % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | REDUCE: (108), (110) imply: % 26.35/4.40 | | | | | | | | (111) $false % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | | CLOSE: (111) is inconsistent. % 26.35/4.40 | | | | | | | | % 26.35/4.40 | | | | | | | End of split % 26.35/4.40 | | | | | | | % 26.35/4.40 | | | | | | End of split % 26.35/4.40 | | | | | | % 26.35/4.40 | | | | | End of split % 26.35/4.40 | | | | | % 26.35/4.40 | | | | Case 2: % 26.35/4.40 | | | | | % 26.35/4.40 | | | | | (112) ~ (all_95_1 = all_48_2) % 26.35/4.40 | | | | | % 26.35/4.40 | | | | | GROUND_INST: instantiating (8) with all_95_1, all_148_2, all_48_1, % 26.35/4.40 | | | | | simplifying with (33), (39) gives: % 26.35/4.40 | | | | | (113) all_148_2 = all_95_1 % 26.35/4.40 | | | | | % 26.35/4.40 | | | | | GROUND_INST: instantiating (8) with all_48_2, all_148_2, all_48_1, % 26.35/4.40 | | | | | simplifying with (39), (41) gives: % 26.35/4.40 | | | | | (114) all_148_2 = all_48_2 % 26.35/4.40 | | | | | % 26.35/4.40 | | | | | COMBINE_EQS: (113), (114) imply: % 26.35/4.40 | | | | | (115) all_95_1 = all_48_2 % 26.35/4.40 | | | | | % 26.35/4.40 | | | | | SIMP: (115) implies: % 26.35/4.40 | | | | | (116) all_95_1 = all_48_2 % 26.35/4.40 | | | | | % 26.35/4.40 | | | | | REDUCE: (112), (116) imply: % 26.35/4.40 | | | | | (117) $false % 26.35/4.40 | | | | | % 26.35/4.40 | | | | | CLOSE: (117) is inconsistent. % 26.35/4.40 | | | | | % 26.35/4.40 | | | | End of split % 26.35/4.40 | | | | % 26.35/4.40 | | | End of split % 26.35/4.40 | | | % 26.35/4.41 | | End of split % 26.35/4.41 | | % 26.35/4.41 | End of split % 26.35/4.41 | % 26.35/4.41 End of proof % 26.35/4.41 % SZS output end Proof for theBenchmark % 26.35/4.41 % 26.35/4.41 3885ms %------------------------------------------------------------------------------